Finite Group Databasebeta

← #14652656

Subgroups — #14652656

Order 2816.

534 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4314C211yesmaximal, characteristic
2#13069551C211yesmaximal, characteristic, complemented
3#13069409C211yesmaximal, characteristic
4C2×#10622122C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic
6C2×#10622092C211yesmaximal, characteristic, complemented
7C2×C11×#334C211yesmaximal, characteristic, complemented
8C22×#4314C411yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66885C411yescharacteristic
15C2×(C2×D11)⋊C8—22no—
16C2×#66881C411yescharacteristic
17C2×#66880C411yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19C2×C4×C11⋊C8C2211yescharacteristic
20C4×#4314—22no—
21C4×#4314—22no—
22C11×#334—22no—
23#10622188—22no—
24#10622122—22no—
25#10622121—22no—
26#10622092—22no—
27C22×D44C2×C411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22C2×C411yescharacteristic
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C22×C8×C11C2×C411yescharacteristic
33C22×C8×C11C2×C411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×C4×Dic11—21no—
40C22×C11⋊C8—21no—
41C22×C11⋊C8D412yes—
42C2×#4314—22no—
43C2×#4314—22no—
44C2×#4314—22no—
45C4×D44—21no—
46C4×D44—21no—
47C4×D44—21no—
48C4×D44—21no—
49C4×Dic22—21no—
50C4×Dic22—21no—
51C4×Dic22—21no—
52C4×Dic22—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C4×C8×C11D412yes—
58C4×C8×C11D412yes—
59#66885—22no—
60(C2×D11)⋊C8—44no—
61#66881—22no—
62#66880—22no—
63C4×C11⋊C8—21no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8—21no—
66C4×C11⋊C8D412yes—
67#9661—111nomaximal, Sylow
68C23×D11—21no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44M1612yes—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C4×D11—42no—
84C2×C4×D11—42no—
85C2×Dic22—21no—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C2×Dic22M1612yes—
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—21no—
94C2×C8×C11—21no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—42no—
98C2×C8×C11—42no—
99C2×C8×C11C22⋊C412yes—
100C2×C8×C11C22⋊C412yes—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113C4×Dic11—41no—
114C4×Dic11—41no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—42no—
119C2×C11⋊C8SD1614yescomplemented
120#4314—28no—
121C2×C4×SD16—111no—
122#1984—111no—
123#1954—111no—
124C2×#334D1111yescharacteristic, complemented
125C2×Q8⋊C8—111no—
126C2×D4⋊C8—111no—
127C2×#322—111no—
128C23×C11C4×D411yescharacteristic
129C22×D11—22no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—42no—
133C22×D11—42no—
134C2×C4×C11—22no—
135C2×C4×C11C2×C22⋊C411yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12411yescharacteristic
140C2×C4×C11#12711yescharacteristic
141C2×C4×C11C2×M1611yescharacteristic
142C2×C4×C11C2×M1611yescharacteristic
143C2×C4×C11#13111yescharacteristic
144C2×C4×C11#13111yescharacteristic
145C2×C4×C11C2×SD1612yes—
146C2×C4×C11#13512yes—
147C2×Dic11—22no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154D44—22no—
155D44—22no—
156D44—41no—
157D44—41no—
158C4×D11—82no—
159C4×D11—81no—
160C4×D11—81no—
161Dic22—22no—
162Dic22—22no—
163Dic22—41no—
164Dic22—41no—
165C8×C11—22no—
166C8×C11—22no—
167C8×C11—81no—
168C8×C11—81no—
169C11⋊C8—24no—
170C11⋊C8—42no—
171C22×SD16—111no—
172C2×C4×Q8—111no—
173C2×C4×D4—111no—
174C4×SD16—222no—
175C4×SD16—222no—
176C2×#106—111no—
177C2×C4⋊C8C2×D1111yescharacteristic
178C2×C4⋊C8C2×D1111yescharacteristic
179C2×#103—111no—
180C2×#102—111no—
181C2×C22⋊C8—222no—
182C2×C4×C8—111no—
183C2×C4×C8—111no—
184C2×C4×C8C2×D1111yescharacteristic
185#336—222no—
186#334—22no—
187Q8⋊C8—222no—
188D4⋊C8—222no—
189#322—222no—
190C22×C11#39011yescharacteristic
191C22×C11#43511yescharacteristic
192C22×C11#43511yescharacteristic
193C22×C11C4×SD1612yes—
194C22×C11#44412yes—
195C2×D11—44no—
196C2×D11—42no—
197C2×D11—82no—
198C2×D11—81no—
199C2×D11—81no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11#40711yescharacteristic
203C4×C11#40811yescharacteristic
204C4×C11#43511yescharacteristic
205C4×C11#43511yescharacteristic
206C4×C11#46512yes—
207C4×C11#49211yescharacteristic
208C4×C11#49511yescharacteristic
209Dic11—42no—
210Dic11—81no—
211Dic11—81no—
212C22×Q8—111no—
213C22×D4—111no—
214C23×C4—221no—
215C2×SD16—222no—
216C2×SD16—222no—
217C2×SD16—222no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—112no—
221C22×C8—221no—
222C22×C8C4×D1111yescharacteristic
223C22×C8C4×D1111yescharacteristic
224C4×Q8—221no—
225C4×Q8—221no—
226C4×Q8—221no—
227C4×Q8—221no—
228C4×D4—221no—
229C4×D4—221no—
230C4×D4—221no—
231C4×D4—221no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C42—221no—
237C2×C42C22×D1111yescharacteristic
238#106—222no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243#103—222no—
244#102—222no—
245C22⋊C8—444no—
246C4×C8—112no—
247C4×C8—221no—
248C4×C8—221no—
249C4×C8—221no—
250C4×C8D4412yes—
251C4×C8C22⋊D1112yes—
252C2×C11#158212yes—
253C2×C11#158312yes—
254C2×C11#195511yescharacteristic
255C2×C11#196811yescharacteristic
256C2×C11#197511yescharacteristic
257D11—82no—
258C24—221no—
259C2×Q8—112no—
260C2×Q8—221no—
261C2×Q8—221no—
262C2×Q8—221no—
263C2×Q8—221no—
264C2×Q8—221no—
265C2×D4—112no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—441no—
275C22×C4—442no—
276C22×C4—442no—
277C22×C4—441no—
278C22×C4C2×C4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280C22×C4#434311yescharacteristic
281SD16—228no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—114no—
291C2×C8—222no—
292C2×C8—222no—
293C2×C8—222no—
294C2×C8—442no—
295C2×C8(C2×D11)⋊C412yes—
296C2×C8(C2×D11)⋊C412yes—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C42—441no—
306C42—441no—
307C42C2×D4411yescharacteristic
308C42D4×D1111yescharacteristic
309C42#434311yescharacteristic
310C42C2×C22⋊D1111yescharacteristic
311C11#966111yescharacteristic, complemented, Sylow
312C23—222no—
313C23—442no—
314C23—442no—
315C23—441no—
316C23—441no—
317C23#6694611yescharacteristic
318Q8—222no—
319Q8—222no—
320Q8—441no—
321Q8—441no—
322D4—222no—
323D4—222no—
324D4—441no—
325D4—441no—
326C2×C4—22no—
327C2×C4—222no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—882no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4#6694611yescharacteristic
338C2×C4#6694811yescharacteristic
339C2×C4#6694811yescharacteristic
340C2×C4#6695411yescharacteristic
341C2×C4#6695411yescharacteristic
342C2×C4M16×D1111yescharacteristic
343C2×C4M16×D1111yescharacteristic
344C2×C4SD16×D1112yes—
345C2×C4#6696912yes—
346C2×C4C2×(C2×D11)⋊C411yescharacteristic
347C2×C4#6699311yescharacteristic
348C2×C4#6700011yescharacteristic
349C8—22no—
350C8—22no—
351C8—81no—
352C8—81no—
353C8—224no—
354C8—442no—
355C22—442no—
356C22—444no—
357C22—881no—
358C22—882no—
359C22—881no—
360C22#1062244911yescharacteristic
361C22#1062244911yescharacteristic
362C22#1062246512yes—
363C22#1062250712yes—
364C22#1062260111yescharacteristic
365C4—21no—
366C4—21no—
367C4—442no—
368C4—881no—
369C4—881no—
370C4#1062244911yescharacteristic
371C4#1062244911yescharacteristic
372C4#1062247712yes—
373C4#1062272311yescharacteristic
374C4#1062273911yescharacteristic
375C4#1062278111yescharacteristic
376C4#1062278811yescharacteristic
377C2—882no—
378C2#1306745112yes—
379C2#1306745812yes—
380C2#1306941311yescharacteristic
381C2#1306946811yescharacteristic
382C2#1306950711yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#334C2
socleC23×C11C4×D4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenterC2×#334D11
hypocenterC11#9661
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#334

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13069551C2semidirect
4. C2×#10622122C2semidirect
6. C2×#10622092C2semidirect
7. C2×C11×#334C2semidirect
119. C2×C11⋊C8SD16semidirect
124. C2×#334D11semidirect
311. C11#9661semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×#43142
#130695512
#130694092
C2×#106221222
C2×#106221212
C2×#106220922
C2×C11×#3342
#966111